LaTeX Symbol Reference

\beta

beta

Lowercase Greek beta. Common variable for regression coefficients and angles.

\gamma

gamma

Lowercase Greek gamma. Used for the gamma function, Euler-Mascheroni constant, and rates.

\delta

delta

Lowercase Greek delta. Used for small differences and Dirac delta.

\epsilon

epsilon (variant)

Lunate (rounded) epsilon. Common in analysis (epsilon-delta) and machine epsilon.

\varepsilon

varepsilon

Classic open epsilon. Many style guides recommend this for error terms.

\zeta

zeta

Lowercase Greek zeta. Used in the Riemann zeta function.

\eta

eta

Lowercase Greek eta. Used for efficiency and viscosity.

\theta

theta

Lowercase Greek theta. Standard angle variable in trigonometry.

\vartheta

vartheta

Script-style theta variant.

\iota

iota

Lowercase Greek iota. Sometimes used for an inclusion map.

\kappa

kappa

Lowercase Greek kappa. Used for curvature and condition number.

\lambda

lambda

Lowercase Greek lambda. Eigenvalues, wavelengths, and rate parameters.

\mu

mu

Lowercase Greek mu. Population mean and friction coefficient.

\nu

nu

Lowercase Greek nu. Frequency and degrees of freedom.

\xi

xi

Lowercase Greek xi. Often used for a random variable.

\pi

pi

Lowercase Greek pi. Ratio of a circle's circumference to its diameter.

\varpi

varpi

Script-style pi variant.

\rho

rho

Lowercase Greek rho. Density and correlation coefficient.

\varrho

varrho

Script-style rho variant.

\sigma

sigma

Lowercase Greek sigma. Standard deviation and stress.

\varsigma

varsigma

Final sigma, used at the end of Greek words but rarely in math.

\tau

tau

Lowercase Greek tau. Time constants and torque.

\upsilon

upsilon

Lowercase Greek upsilon.

\phi

phi

Lowercase Greek phi. Golden ratio and Euler totient.

\varphi

varphi

Open-style phi variant.

\chi

chi

Lowercase Greek chi. Used in chi-squared tests.

\psi

psi

Lowercase Greek psi. Wave function in quantum mechanics.

\omega

omega

Lowercase Greek omega. Angular frequency.

\Gamma

Gamma

Uppercase Greek Gamma. Gamma function notation.

\Delta

Delta

Uppercase Greek Delta. Difference operator and Laplacian.

\Theta

Theta

Uppercase Greek Theta. Big-Theta complexity.

\Lambda

Lambda

Uppercase Greek Lambda. Cosmological constant.

\Xi

Xi

Uppercase Greek Xi.

\Pi

Pi

Uppercase Greek Pi. Product operator when used as \prod.

\Sigma

Sigma

Uppercase Greek Sigma. Sum operator when used as \sum.

\Upsilon

Upsilon

Uppercase Greek Upsilon.

\Phi

Phi

Uppercase Greek Phi. Cumulative normal distribution.

\Psi

Psi

Uppercase Greek Psi.

\Omega

Omega

Uppercase Greek Omega. Big-Omega complexity and ohms.

+

plus

Addition operator. Use directly in math mode.

-

minus

Subtraction operator. LaTeX renders the proper minus glyph in math mode.

\pm

plus or minus

Plus-or-minus sign for tolerances and quadratic roots.

\mp

minus or plus

Minus-or-plus sign, the complement of \pm.

\times

times

Multiplication cross.

\cdot

centered dot

Centered dot for multiplication, scalar product, and function composition.

\div

division sign

Obelus division sign. Most modern style guides prefer \frac{a}{b}.

\frac{a}{b}

fraction

Stacked fraction with numerator and denominator. Renders larger in display mode.

\sqrt{x}

square root

Square root with automatic sizing.

\sqrt[n]{x}

nth root

Nth root. The optional index appears above the radical.

x^{n}

superscript

Superscript / exponent. Always wrap multi-character exponents in braces.

x_{n}

subscript

Subscript. Always wrap multi-character subscripts in braces.

\sum_{i=1}^{n}

sum

Summation big operator. Limits appear above and below in display mode.

\prod_{i=1}^{n}

product

Product big operator.

\coprod

coproduct

Coproduct / disjoint union big operator.

\int

integral

Indefinite integral.

\int_{a}^{b}

definite integral

Definite integral with lower and upper limits.

\iint

double integral

Double integral.

\iiint

triple integral

Triple integral.

\oint

contour integral

Contour integral over a closed curve.

\bigcup

big union

Indexed union big operator.

\bigcap

big intersection

Indexed intersection big operator.

\bigoplus

big direct sum

Direct sum big operator.

\bigotimes

big tensor product

Tensor product big operator.

\circ

ring composition

Function composition, e.g. (f \circ g)(x).

\bullet

bullet

Solid bullet operator.

\ast

asterisk

Math-mode asterisk, larger than the text-mode *.

\star

star

Five-pointed star operator.

\sin

sine

Sine function, typeset upright as is convention for named functions.

\cos

cosine

Cosine function.

\tan

tangent

Tangent function.

\log

logarithm

Logarithm; base goes in subscript.

\ln

natural log

Natural logarithm.

\exp

exponential

Exponential function.

\lim_{x \to 0}

limit

Limit. Subscript appears below in display mode.

\max

maximum

Maximum.

\min

minimum

Minimum.

=

equals

Equality. Use directly.

\neq

not equal

Inequality. Also \ne.

\equiv

identical

Identically equal / congruent.

\approx

approximately equal

Approximately equal.

\sim

similar / distributed as

Tilde used for similarity and 'is distributed as' in statistics.

\simeq

similar equal

Asymptotically equal.

\cong

congruent

Geometrically congruent.

\propto

proportional to

Proportional to.

<

less than

Less than.

>

greater than

Greater than.

\leq

less than or equal

Less than or equal. Also \le.

\geq

greater than or equal

Greater than or equal. Also \ge.

\ll

much less than

Much less than.

\gg

much greater than

Much greater than.

\prec

precedes

Precedes / comes before in an order.

\succ

succeeds

Succeeds / comes after in an order.

\parallel

parallel to

Parallel lines.

\nparallel

not parallel

Not parallel. Needs the amssymb package.

\usepackage{amssymb}

\perp

perpendicular to

Perpendicular to.

\mid

divides

Divides / 'such that' in set-builder notation.

\nmid

does not divide

Does not divide. Needs amssymb.

\usepackage{amssymb}

\doteq

approximately equals (dot)

Equals by definition.

\leftarrow

left arrow

Single left arrow. Also written as \gets.

\rightarrow

right arrow

Single right arrow. Also written as \to.

\leftrightarrow

left-right arrow

Bidirectional single arrow.

\Leftarrow

double left arrow

Double left arrow, often read 'is implied by'.

\Rightarrow

double right arrow

Double right arrow, often read 'implies'.

\Leftrightarrow

double left-right arrow

Double bidirectional arrow, 'if and only if'.

\uparrow

up arrow

Single up arrow.

\downarrow

down arrow

Single down arrow.

\updownarrow

up-down arrow

Bidirectional vertical arrow.

\Uparrow

double up arrow

Double up arrow.

\Downarrow

double down arrow

Double down arrow.

\longleftarrow

long left arrow

Extended left arrow.

\longrightarrow

long right arrow

Extended right arrow.

\longleftrightarrow

long left-right arrow

Extended bidirectional arrow.

\Longleftarrow

long double left arrow

Extended double left arrow.

\Longrightarrow

long double right arrow

Extended double right arrow.

\Longleftrightarrow

long double left-right arrow

Extended double bidirectional arrow.

\mapsto

maps to

Used to define a function: x \mapsto x^2.

\longmapsto

long maps to

Extended 'maps to' arrow.

\hookrightarrow

hook right arrow

Inclusion / embedding.

\hookleftarrow

hook left arrow

Mirror of \hookrightarrow.

\rightharpoonup

right harpoon up

Right harpoon with barb upward.

\rightharpoondown

right harpoon down

Right harpoon with barb downward.

\rightleftharpoons

reversible reaction

Right and left harpoons stacked, used for chemical equilibria.

\in

element of

Set membership.

\notin

not an element of

Negation of \in.

\ni

contains as element

Reverse membership.

\subset

subset of

Proper subset.

\supset

superset of

Proper superset.

\subseteq

subset or equal

Subset or equal to.

\supseteq

superset or equal

Superset or equal to.

\subsetneq

proper subset

Subset, not equal. Needs amssymb.

\usepackage{amssymb}

\nsubseteq

not a subset

Not a subset. Needs amssymb.

\usepackage{amssymb}

\cup

union

Set union.

\cap

intersection

Set intersection.

\setminus

set minus

Set difference (A \setminus B). Visually distinct from a backslash.

\emptyset

empty set

Empty set.

\varnothing

empty set (variant)

Stylish empty set, often preferred in formal proofs. Needs amssymb.

\usepackage{amssymb}

\mathbb{N}

natural numbers

Blackboard-bold N. Needs amssymb (or amsfonts).

\usepackage{amssymb}

\mathbb{Z}

integers

Blackboard-bold Z for integers.

\usepackage{amssymb}

\mathbb{Q}

rational numbers

Blackboard-bold Q for rationals.

\usepackage{amssymb}

\mathbb{R}

real numbers

Blackboard-bold R for reals.

\usepackage{amssymb}

\mathbb{C}

complex numbers

Blackboard-bold C for complex numbers.

\usepackage{amssymb}

\forall

for all

Universal quantifier.

\exists

there exists

Existential quantifier.

\nexists

there does not exist

Negated existential. Needs amssymb.

\usepackage{amssymb}

\land

and (logical)

Logical conjunction.

\lor

or (logical)

Logical disjunction.

\neg

not (logical)

Logical negation.

\implies

implies

Material implication, equivalent to \Longrightarrow but reads as 'implies'.

\iff

if and only if

Biconditional, equivalent to \Longleftrightarrow.

\vdash

proves / turnstile

Syntactic entailment / 'proves'.

\models

models / entails

Semantic entailment / 'models'.

\therefore

therefore

Therefore.

\because

because

Because.

\partial

partial derivative

Partial differential operator.

\nabla

nabla / del

Gradient operator.

\infty

infinity

Infinity.

\to

to / tends to

Right arrow, commonly read as 'tends to' in limits.

\limsup

limit superior

Limit superior.

\liminf

limit inferior

Limit inferior.

\sup

supremum

Supremum / least upper bound.

\inf

infimum

Infimum / greatest lower bound.

\sum_{n=0}^{\infty}

infinite sum

Sum to infinity. Combine \sum with \infty.

\bar{x}

bar (mean)

Sample mean. Renders a horizontal bar above x.

\hat{x}

hat (estimate)

Estimator notation.

\tilde{x}

tilde

Approximation or median notation.

\mathbb{E}[X]

expected value

Blackboard-bold E for expectation. Needs amssymb.

\usepackage{amssymb}

\mathrm{Var}(X)

variance

Variance. \mathrm forces upright text.

\mathrm{Cov}(X,Y)

covariance

Covariance.

P(A \mid B)

conditional probability

Conditional probability uses \mid for the vertical bar.

X \sim N(\mu, \sigma^2)

distributed as

X is distributed as a normal with parameters mu and sigma squared.

( )

parentheses

Plain parentheses. Use \left( and \right) for auto-sizing.

[ ]

square brackets

Square brackets.

\{ \}

curly braces

Curly braces. Escape with backslashes because {} are LaTeX group markers.

\langle x \rangle

angle brackets

Angle brackets, used for inner products.

\lvert x \rvert

absolute value

Absolute value. Better than typing | because it gets correct spacing.

\lVert x \rVert

norm

Vector norm.

\lfloor x \rfloor

floor

Floor (round down).

\lceil x \rceil

ceiling

Ceiling (round up).

\left( \frac{a}{b} \right)

auto-sizing pair

Wrap delimiters in \left and \right so they grow to match their content.

\overbrace{abc}^{n}

overbrace

Brace above an expression with an optional label.

\underbrace{abc}_{n}

underbrace

Brace below an expression with an optional label.

\hat{a}

hat

Hat accent. Use \widehat for wider expressions.

\widehat{abc}

wide hat

Hat over multi-character expression.

\bar{a}

bar

Bar accent. Use \overline for wider expressions.

\overline{abc}

overline

Line above a multi-character expression. Often used for complex conjugates.

\underline{abc}

underline

Line below a multi-character expression.

\tilde{a}

tilde

Tilde accent. Use \widetilde for wider expressions.

\widetilde{abc}

wide tilde

Tilde over multi-character expression.

\dot{a}

dot

Single dot, used in physics for time derivatives.

\ddot{a}

double dot

Double dot, second time derivative.

\vec{a}

vector arrow

Vector accent (small right arrow).

\overrightarrow{AB}

right arrow over

Right arrow over a multi-character expression.

a'

prime

Single prime, often used for derivatives.

a''

double prime

Double prime.

\pi

pi (constant)

Mathematical constant pi.

\infty

infinity (constant)

Infinity.

\aleph

aleph

First letter of the Hebrew alphabet, used for cardinal numbers (\aleph_0 reads 'aleph null').

\hbar

hbar (reduced Planck)

Reduced Planck constant.

\imath

dotless i

Italic i without a dot, often used for the imaginary unit when overlaid with \hat.

\jmath

dotless j

Italic j without a dot.

\Re

real part

Real part of a complex number.

\Im

imaginary part

Imaginary part of a complex number.

\angle

angle

Angle symbol.

\measuredangle

measured angle

Measured angle. Needs amssymb.

\usepackage{amssymb}

\degree

degree

Degree symbol. Needs the gensymb package, or use ^{\circ} for a math-mode version.

\usepackage{gensymb}

^{\circ}

degree (circ)

Math-mode degree symbol without an extra package.

\prime

prime symbol

Standalone prime symbol; usually you just type ' instead.

\dagger

dagger

Dagger, often used for adjoints in physics.

\ddagger

double dagger

Double dagger.

\square

square

Empty square, used for QED in proofs.

\usepackage{amssymb}

\blacksquare

filled square

Filled square, the traditional 'end of proof' (QED) marker.

\usepackage{amssymb}

\mathbf{x}

bold (math)

Bold math letter, typically for vectors and matrices.

\mathit{x}

italic (math)

Italic math letter (the default for variables).

\mathrm{x}

roman (upright)

Upright Roman letter, used for named functions and units.

\mathsf{x}

sans-serif

Sans-serif math letter.

\mathtt{x}

typewriter

Monospaced math letter.

\mathcal{F}

calligraphic

Calligraphic capital (script-like). Works for uppercase letters only.

\mathscr{F}

script

Formal script capital. Needs the mathrsfs package.

\usepackage{mathrsfs}

\mathbb{R}

blackboard bold

Blackboard-bold capital for number sets. Needs amsfonts or amssymb.

\usepackage{amssymb}

\mathfrak{A}

fraktur

Fraktur (Gothic) capital, used for Lie algebras and ideals. Needs amsfonts.

\usepackage{amsfonts}

\boldsymbol{\alpha}

bold symbol

Bold versions of Greek letters and other math symbols.

\,

thin space

Small positive horizontal space.

\:

medium space

Medium positive horizontal space.

\;

thick space

Thick positive horizontal space.

\!

negative thin space

Small negative horizontal space, useful to tighten subscripts.

\quad

quad

1 em of space.

\qquad

double quad

2 em of space.

\\

line break

Forced line break inside arrays, tables, and align environments.

\newline

newline

Same as \\ outside math mode.

~

non-breaking space

Non-breaking space. The line will not break between words joined by ~.